Final answer:
By standardizing the values, we can find the probability using a standard normal distribution table or calculator. The probability is approximately 0.9798 or 97.98%.
Step-by-step explanation:
To find P(395.4 < x < 404.6), we can first standardize the values using the standard deviation of the sample mean. The formula for the standard deviation of the sample mean is σ / √n, where σ is the population standard deviation and n is the sample size.
So, the standard deviation of the sample mean is 20 / √100 = 2.
Next, we standardize the values 395.4 and 404.6 using the sample mean and the standard deviation of the sample mean:
Z1 = (395.4 - 400) / 2
= -2.3
Z2 = (404.6 - 400) / 2
= 2.3
Now, we can use a standard normal distribution table or a calculator to find the probability between -2.3 and 2.3.
The table or calculator will give us a value of approximately 0.9798.
Therefore, P(395.4 < x < 404.6) is approximately 0.9798, or 97.98%.